1. Field
This application relates to static geometric space defining structures, specifically to such structures which utilize hyperbolic paraboloids. In particular, this application relates to use of any of the three different hyperbolic paraboloids that divide a Correlating Tetrahedron (CT) in half.
2. Prior Art
This application is a substitute for application Ser. No. 12,395,974 necessitated by the discovery of significant new uses of this technology. Also, about two years after filing application Ser. No. 12,395,974, the applicant discovered that Peter Pearce, in his book Structure in Nature is a Strategy for Design, had independently discovered what the applicant calls a 4-fold hyperbolic paraboloid—Pearce called it a saddle tetrahedron. This discovery was disclosed to the USPTO as required. Several significant new uses of the 4-fold hyperbolic paraboloid are disclosed in this application and claimed as new uses.
The tetrahedron has been commonly used in trusses. The regular tetrahedron, which is one of the five platonic solids, is composed of four faces that are equilateral triangles, six edges between these faces, and four vertices where the corners of three triangular faces meet. This regular tetrahedron is not included in the technology of this application. The Correlating Tetrahedrons (CTs) of this application all have isosceles triangular faces with one L2 edge and two L1 edges (the L1 and L2 edges are further defined later in this specification). During pursuit of a light weight tetrahedral structure, the applicant discovered the multitude of ways the hyperbolic paraboloids which divide the CT in half can be used as structural members to create new composite structures.
Tetrahedrons have been used in trusses where a frame composed of structural members along each edge of the tetrahedron result in four vertices and multiple tetrahedrons are attached at their vertices and/or edges to build a strong truss. What has not been recognized is the utility of using the hyperbolic paraboloids which divide a special set of these tetrahedrons in half. The special Correlating Tetrahedrons (CTs) of this application are divided in half by hyperbolic paraboloids whose edge dimensions and spatial arrangement are thus defined by the CT.
Unexpectedly, these CT hyperbolic paraboloids can be utilized to make a multitude of new, unique geometric structures which, in some applications, can be fit together in a joint that has superior interlocking attributes due to the saddle shaped compound curvature of the CT hyperbolic paraboloids. In other applications the hyperbolic paraboloids of the CT can be used to create cellular, repeating lattice or labyrinthal structures. All of the structures of this application effectively harness the superior rigidity resulting from the smooth saddle shaped compound curvature of the CT hyperbolic paraboloids. This curvature results in improved rigidity similar to the improved rigidity that results from a sheet of paper formed into a cylinder which is more rigid than a flat sheet, yet both have the same thickness.
The new technology which is the subject of this application is described in detail below.